SPH3U1 - Energy Problems Set 4
Problems
1. Write the nuclear reaction
equation for the following nuclei
undergoing the indicated type of
decay:
a.
b.
c.
d.
e.
f.
g.
h.
Nucleus
Polonium-210
Calcium-45
Chromium-46
Dysprosium-152
Plutonium-240
Copper-58
Bismuth-214
Sodium-22
Decay type
alpha decay
beta-negative decay
beta-positive decay
γ decay
α decay
gamma decay
β- decay
β+decay
2. The following shows the products of part of a decay series known as the Thorium
Series. Write a nuclear reaction equation for each decay stage of the series and
identify its type.
232
228
228
228
220
224
90𝑇ℎ → 88𝑅𝑎 → 89𝐴𝑐 → 90𝑇ℎ → 88𝑅𝑎 → 86𝑅𝑛
Half-life
3. The half-life of carbon-14 is 5730 a. An ancient piece of bark is estimated to have
originally contained 2.00 µg of carbon-14. If its age has been determined to be
1.7x104 a, how much carbon-14 does it now have?
4. A specimen of peat from an ancient bog contains 800.0 µg of carbon-14. What will
be the amount of carbon-14 remaining after 1.0 x104 a?
5. Uranium-238 has a half-life of 4.468x109 a. A sample of uranium ore currently has
722 mg of uranium-238. If the sample is 5.9x108 a, how much uranium-238 was
there when it formed?
6. Iodine 131
53𝐼 is used in diagnostic and therapeutic techniques in the treatment of
thyroid disorders. This isotope has a half-life of 8.04 days. What percentage of an
initial sample of 131
53𝐼 remains after 30.0 days?
7. To make the dial of a watch glow in the dark, 1.000 ×10-9 kg of radium 226
88𝑅𝑎 is
3
used. The half-life of this isotope has a value of 1.60 ×10 yr. How many kilograms
of radium disappear while the watch is in use for fifty years?
SPH3U1 - Energy Problems Set
8. The shroud of Turin is a religious artefact known since the Middle Ages. In 1988 its
age was measured using the radiocarbon dating technique, which revealed that
the shroud could not have been made before 1200 AD. Of the 146𝐶 nuclei that
were present in the living matter from which the shroud was made, what
percentage remained in 1988?
Nuclear Fission
9. During a nuclear reaction, an unknown particle is absorbed by a copper 63
29𝐶𝑢
62
nucleus, and the reaction products are 29𝐶𝑢, a neutron, and a proton. Determine
the unknown particle and the nucleus temporarily formed when the copper 63
29𝐶𝑢
nucleus absorbs the unknown particle.
10. A neutron causes 232
90𝑇ℎ to fission according to the reaction
232
1
𝐴
90𝑇ℎ + 0𝑛 → 𝑍𝑋 + 𝛾
a. Identify the unknown nucleus , giving its atomic mass number A, its atomic
number Z, and the symbol X for the element.
b. Nucleus X then undergoes β- decay, and its daughter does too. Identify the
final nucleus, giving its atomic mass number, atomic number, and name.
11.A small sample of coal, when completely converted to energy, releases 4.5 × 1014 J
of energy. Determine the original mass of coal, assuming the final mass is zero.
12.Calculate the mass defect, in kilograms, and the energy released, in joules, of the
following nuclear reaction:
140
235
93
1
1
92𝑈 + 0𝑛 → 55𝐶𝑠 + 37𝑅𝑏 + 3 0𝑛
235
92𝑈
= 235.044 𝑢,
1
0𝑛
= 1.009 𝑢,
140
55𝐶𝑠
= 139.909 𝑢,
93
37𝑅𝑏
= 92.922 𝑢
13.How much energy, in MeV, is released by the following fission reaction?
235
92𝑈
235
92𝑈
= 235.044 𝑢,
1
0𝑛
+ 10𝑛 →
= 1.009 𝑢,
94
38𝑆𝑟
1
+ 140
54𝑋𝑒 + 2 0𝑛
96
38𝑆𝑟
= 93.915 𝑢,
140
54𝑋𝑒
= 139.922 𝑢
SPH3U1 - Energy Problems Set
2
14.The energy released during each 235
92𝑈 fission is 2.0 × 10 MeV. How many
kilograms of coal must be burned to produce the same energy as 1.0 kg of 235
92𝑈 if
7
3.0 × 10 J of energy is released when 1.0 kg of coal is burned?
(n.b. 2.6 x1024
U nuclei are found in a 1 kg sample of uranium)
Nuclear Fusion
15.One reaction to produce carbon in stars is as follows:
4
2𝐻𝑒
+ 42𝐻𝑒 + 42𝐻𝑒 →
12
6𝐶
Calculate the mass defect, in atomic mass units, and energy released, in
12
electronvolts, of this reaction.
( 42𝐻𝑒 m=4.002603 u,
6𝐶 m = 12.00000 u)
16.Consider the induced nuclear reaction 21𝐻 + 147𝑁 → 126𝐶 + 42𝐻𝑒 . The atomic
masses are 21𝐻 (2.014 102 u), 147𝑁 (14.003 074 u), 126𝐶 (12.000 000 u), and 42𝐻𝑒
(4.002 603 u). Determine the energy released, in joules, when the 126𝐶 and 42𝐻𝑒
nuclei are formed in this way.
17.Two deuterium atoms ( 21𝐻= 2.014102 u) react to produce tritium
( 31𝐻= 3.016050 u) and hydrogen ( 11𝐻= 1.007825 u) according to the reaction:
2
1𝐻
+ 21𝐻 → 31𝐻 + 11𝐻
What is the energy released by this deuterium-deuterium reaction?
18.One proposed fusion reaction combines lithium 63𝐿𝑖 (6.015 u) with deuterium 21𝐻
(2.014 u) to give helium 42𝐻𝑒 (4.003 u):
2
1𝐻
+ 63𝐿𝑖 → 2 42𝐻𝑒
a) How many of the above reactions would need to occur to supply the energy
needs of one household for a year (estimated to be 3.8 × 1010 J)?
b) How many grams of lithium would be needed if there are 8.673x1025 Li nuclei
in 1 kg of a lithium sample?
SPH3U1 - Energy Problems Set
19.The following shows the carbon-nitrogen-oxygen (CNO) cycle that occurs inside
stars. Write a nuclear reaction equation for each stage in the cycle and identify its
type.
13
13
15
15
12
14
12
4
6𝐶 → 7𝑁 → 6𝐶 → 7𝑁 → 8𝑂 → 7𝑁 → 6𝐶 + 2𝐻𝑒
Conceptual Questions
1. To which of the following objects, each about 1000 yr old, can the radiocarbon
dating technique not be applied: a wooden box, a gold statue, and some plant
seeds? Explain.
2. Some preserved seed were found and their age, through the technique of carbon
dating, was determined to be 5000 years old. However, new evidence suggests
that the amount of carbon in the air at that time is higher than previously
thought. Are the seeds older or younger than 5000 years? Explain.
3. Compare and contrast nuclear fission and fusion. How are they alike? How are
they different?
4. Why are neutrons such good projectiles for producing nuclear reactions?
5. Explain why nuclear fusion is much more difficult to obtain than nuclear fission
6. Why is nuclear fusion more desirable than nuclear fission for power generation?
Explain.
7. The energy from nuclear fission appears in the form of thermal energy – but the
thermal energy of what? Explain.
SPH3U1 - Energy Problems Set
ANSWERS
3. 0.26 µg
4. 240 µg
5. 790 mg
6. 7.53 %
7. 2.14 x10-11 kg
8. 91 %
9. p+, 64
30𝑍𝑛
233
10. a) 90𝑇ℎ
b) 233
92𝑈
11. 5.0 g
12. 3.237 x10-28 kg, 2.91x10-11 J
13. 184 MeV
14. 2.8 x106 kg
15. 7.8 x10-3 u, 7.3 x106 eV
16. 2.2 x10-12 J
17. 4.0 MeV, 6.4 x10-13 J
18. a) 1.1 x1022 reactions
b) 0.13 g